{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# High Order Symplectic Integrators\n",
    "\n",
    "These notebooks show how to use the high order symplectic integrators of Wisdom et al. (1996) and Laskar & Robutel (2001) with REBOUND. See  Rein, Tamayo & Brown (2019) for an overview of these integrators. \n",
    "\n",
    "Let us start by importing REBOUND, as well as numpy and matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import rebound\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "High order symplectic integrators with a fixed timestep are well suited for planetary systems in which planets orbit the primary mass on almost Keplerian orbits. The planet-planet interactions need to be a perturbation. If they are not, a different integrator, such as IAS15 or MERCURIUS is better suited.\n",
    "\n",
    "On system that we know is stable is the outer Solar System. So we will use this as our test case. We can either import accurate data from NASA Horizons, or, because this is just a test, use some of the initial conditions which come with REBOUND to setup a simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<rebound.plotting.OrbitPlot at 0x104d06d00>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from rebound import data\n",
    "sim = rebound.Simulation()\n",
    "data.add_outer_solar_system(sim) # either this, or add the planets manually\n",
    "rebound.OrbitPlot(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll integrate the outer Solar System for 1000 years into the future and measure the energy error along the way. We do that at random intervals to make sure we don't have any aliasing with an orbital period. The following function runs the simulation, and then returns the error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def measure_energy(sim):\n",
    "    Nsamples = 1000\n",
    "    tmax = 2.*np.pi*1e3 # 1000 years\n",
    "    t_samples = tmax*np.sort(np.random.random(Nsamples))\n",
    "    E0 = sim.energy() # initial energy\n",
    "    Emax = 0. # maximum energy error\n",
    "    for t in t_samples:\n",
    "        # we do not want to change the timestep to reach t exactly, thus \n",
    "        # we need to set exact_finish_time=False and slighlty overshoot.\n",
    "        sim.integrate(t,exact_finish_time=False) \n",
    "        E = sim.energy()\n",
    "        Emax = max(Emax, np.abs((E-E0)/E0))\n",
    "    return Emax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get an idea how our integrators are behaving, we want to run this simulation for various timesteps. So let us set up an array of timesteps from 0.001 to 1 orbital periods of Jupiter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_dt_samples = 100\n",
    "dt_samples = sim.particles[1].P * np.logspace(-3,0.,N_dt_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run the simulations with the standard WH integrator first. We set `safe_mode` to 0 to speed up the calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Emax_wh = np.zeros(N_dt_samples)\n",
    "for i, dt in enumerate(dt_samples):\n",
    "    sim_run = sim.copy() # make a copy of the simulation so we don't need to set a new one up every time\n",
    "    sim_run.integrator = \"whfast\"\n",
    "    sim_run.dt = dt\n",
    "    sim.ri_whfast.safe_mode = False\n",
    "    Emax_wh[i] = measure_energy(sim_run)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f,ax = plt.subplots(1,1,figsize=(7,5))\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(\"timestep [Jupiter years]\")\n",
    "ax.set_ylabel(\"relative energy error\")\n",
    "ax.plot(dt_samples/sim.particles[1].P,Emax_wh,label=\"WH\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the WH converges quadratically and reaches a precision of $10^{-9}$ at a timestep of 0.001 Jupiter years. Let's try the same with the WHCKL, SABACL4, and SABA(10,6,4) integrators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rein/git/rebound/rebound/simulation.py:724: RuntimeWarning: WHFast convergence issue. Timestep is larger than at least one orbital period.\n",
      "  warnings.warn(msg[1:], RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "Emax_saba4 = np.zeros(N_dt_samples)\n",
    "for i, dt in enumerate(dt_samples):\n",
    "    sim_run = sim.copy() # make a copy of the simulation so we don't need to set a new one up every time\n",
    "    sim_run.integrator = \"SABACL4\"\n",
    "    sim_run.ri_saba.safe_mode = False\n",
    "    sim_run.dt = dt\n",
    "    Emax_saba4[i] = measure_energy(sim_run)\n",
    "Emax_saba1064 = np.zeros(N_dt_samples)\n",
    "for i, dt in enumerate(dt_samples):\n",
    "    sim_run = sim.copy() \n",
    "    sim_run.integrator = \"SABA(10,6,4)\" \n",
    "    sim_run.ri_whfast.safe_mode = False\n",
    "    sim_run.dt = dt\n",
    "    Emax_saba1064[i] = measure_energy(sim_run)\n",
    "Emax_whckl = np.zeros(N_dt_samples)\n",
    "for i, dt in enumerate(dt_samples):\n",
    "    sim_run = sim.copy() \n",
    "    sim_run.integrator = \"WHCKL\" \n",
    "    sim_run.ri_whfast.safe_mode = False\n",
    "    sim_run.dt = dt\n",
    "    Emax_whckl[i] = measure_energy(sim_run)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a warning message because the largest timestep we try is larger than the innermost orbital period. You would not want to use such a large timestep in an actual simulation, but we can ignore the message for this test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f,ax = plt.subplots(1,1,figsize=(7,5))\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(\"timestep [Jupiter years]\")\n",
    "ax.set_ylabel(\"relative energy error\")\n",
    "ax.plot(dt_samples/sim.particles[1].P,Emax_wh,label=\"WH\")\n",
    "ax.plot(dt_samples/sim.particles[1].P,Emax_saba4,label=\"SABACL4\")\n",
    "ax.plot(dt_samples/sim.particles[1].P,Emax_whckl,label=\"WHCKL\")\n",
    "ax.plot(dt_samples/sim.particles[1].P,Emax_saba1064,label=\"SABA(10,6,4)\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the higher order SABA4, WHCKL, and SABA(10,6,4) integrators are doing significantly better than the standard WH method. For very small timesteps the methods are limited by double floating point precision. The SABA methods appear to be slightly better than the WHCKL method above, but note that the SABA methods are also much slower than the WHCKL per timestep. Taking this into account, the WHCKL has a slight advantage for timesteps larger than 1% of the shortest orbital period. For extremely high accuracy, the SABA(10,6,4) method is faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that by default all integrators set `safe_mode=False` and `keep_unsynchronized=False`. Depending on your application, you might want to change these flags."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
